Final answer:
The bond will take approximately 12.5 years to mature.
Step-by-step explanation:
The bond matures when the investor receives the face value of $1,000 at the end of its term. To calculate the number of years until maturity, we need to find the present value of the bond using the yield to maturity. The present value of the bond is calculated as follows:
Present Value = Coupon Payment * (1 - (1 + r/n)^(-nt)) / (r/n) + Face Value / (1 + r/n)^nt
In this case, the present value is $760.50 and the yield to maturity is 8.52%. By plugging in these values along with the coupon payment of $40 (6.4% of $1,000), the number of periods (nt), and the interest rate (r/n), we can solve for the number of years until maturity.
By solving the equation, we find that it will take approximately 12.5 years for this bond to mature.
To calculate the remaining years until the bond matures, one would typically use the present value formula for bonds, which accounts for the present value of the bond's future coupon payments and the bond's face value at maturity, discounted at the bond's current yield to maturity. However, since the question does not provide all the necessary data to perform this calculation directly, this appears to be a conceptual question hinting at the relationship between bond prices, yield to maturity, interest rates, and time to maturity.